A Thermal–Hydraulic–Mechanical–Chemical Coupling Model for Acid Fracture Propagation Based on a Phase-Field Method.

Acid fracturing is a technique to enhance productivity in carbonate formations. In this work, a thermal–hydraulic–mechanical–chemical (THMC) coupling model for acid fracture propagation is proposed based on a phase-field approach. The phase-field variable is utilized as an indicator function to distinguish the fracture and the reservoir, and to track the propagation of the fracture. The resulting system is a nonstationary, nonlinear, variational inequality system in which five different physical modules for the displacement, the phase-field, the pressure, the temperature, and the acid concentration are coupled. This multi-physical system includes numerical challenges in terms of nonlinearities, solution coupling algorithms, and computational cost. To this end, high fidelity physics-based discretizations, parallel solvers, and mesh adaptivity techniques are required. The model solves the phase-field and the displacement variables by a quasi-monolithic scheme and the other variables by a partitioned schemes, where the resulting overall algorithm is of iterative coupling type. In order to maintain the computational cost low, the adaptive mesh refinement technique in terms of a predictor-corrector method is employed. The error indicators are obtained from both the phase-field and concentration approximations. The proposed model and the computational robustness were investigated by studying fourteen cases as well as some mesh refinement studies. It is observed that the acid and thermal effect increase the fracture volume and fracture width. Moreover, the natural fractures and holes affect the acid fracture propagation direction. Highlights: thermal–hydraulic–mechanical–chemical coupling system was established for acid fracture propagation based on a phase-field method. The acid fluid equations including diffusion, transport and reaction were derived. The penalization method was introduced based on physical reality. Acid fracture problem is a kind of dynamic heterogeneous problem. The adaptive mesh refinement was extended to help researchers get smooth simulation results and save computation costs. [ABSTRACT FROM AUTHOR]